OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
R(n,k,m) = k*Sum_{i=0..n-k} binomial(i+m-1, m-1)*binomial(2*(n-i)-k-1, n-i-1)/(n-i), m = 2, k > 0.
R(n,0,2) = n + 1.
EXAMPLE
Array begins
1;
2, 1;
3, 3, 1;
4, 7, 4, 1;
5, 16, 12, 5, 1;
6, 39, 34, 18, 6, 1;
7, 104, 98, 59, 25, 7, 1;
8, 301, 294, 190, 92, 33, 8, 1;
Production matrix begins:
2, 1;
-1, 1, 1;
1, 1, 1, 1;
0, 1, 1, 1, 1;
0, 1, 1, 1, 1, 1;
0, 1, 1, 1, 1, 1, 1;
0, 1, 1, 1, 1, 1, 1, 1;
0, 1, 1, 1, 1, 1, 1, 1, 1;
... Philippe Deléham, Sep 20 2014
MATHEMATICA
r[n_, k_, m_] := k*Sum[ Binomial[i + m - 1, m - 1]*Binomial[2*(n - i) - k - 1, n - i - 1]/(n - i), {i, 0, n - k}]; r[n_, 0, 2] := n + 1; Table[r[n, k, 2], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Dec 13 2012, from formula *)
PROG
(Sage)
@CachedFunction
def A(n, k):
if n==k: return n+1
return add(A(n-1, j) for j in (0..k))
A185943 = lambda n, k: A(n, n-k)
for n in (0..7) :
print([A185943(n, k) for k in (0..n)]) # Peter Luschny, Nov 14 2012
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Vladimir Kruchinin, Feb 07 2011
STATUS
approved